In a secret ballot late on Tuesday, 348 lawmakers in the 550-seat parliament voted for Erdogan’s plan to lift MPs' immunity from prosecution, which could be used to target the pro-Kurdish opposition, Peoples' Democratic Party (HDP).
The assembly will now vote on the amendment in a second round of voting on Friday.
The Justice and Development Party (AKP) needs 367 votes to change the constitution directly 330 votes or at least 330 to put the measure to a referendum.
The left-wing HDP, which is the third-largest grouping in the Turkish parliament, has said the move is aimed at undermining its support and could disenfranchise its voters, drawn mainly from Turkey's Kurdish minority of 15 million people. The HDP has said an overwhelming majority of its 59 deputies could be jailed, mostly for views they have expressed, virtually wiping out its parliamentary presence.
President Tayyip Erdogan and the AKP, which he founded, accuse the HDP of serving as the political wing of the armed Kurdistan Workers Party (PKK), listed by Turkey as a terrorist organization. The HDP denies this.
Lawmakers currently enjoy immunity from prosecution. The new law will allow prosecutors to purse members of parliament who currently face investigation: 138 deputies, of whom 100 are from the HDP and main opposition Republican People's Party (CHP).